CETE
Méditerranée
A combined model distribution-assignment
constrained by travel time
20th international
EMME/2 users’
conference
19/10/06
Presented by M. Mariotto
CETE
Who we are - n°1
Méditerranée
The C.E.T.E. Méditerranée
1 / 7 technical centers of the French transport ministry
- in charge of the East-Southern French regions (600
employees)
- a consultant company working in the competitive
sector
- in the fields of :
-
Transports development, politics and planning
• Environment, territories development, urban economy
• Risks management
• Road management
• Civil engineering
• Earth observation
• Geotechnical works
•
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CETE
Who we are - n°2
Méditerranée
My team
in charge of urban traffic studies and transport
planning
- in the field of modelling, 4 people (1 engineer and 3
technicians) working on :
- model buildings
-
(monomodal models principally)
-
traffic studies and transport plans
(new facility effects for example, static and dynamic approach, but mainly with auto mode)
-
audit of model developments
(on multimodal models for instance)
-
development of new approaches
(2 studies with AIMSUN combined with former models developed on EMME/2)
3/31
CETE
Starting point - n°1
Méditerranée
Background
We are in charge of one of the models used to
forecast urban traffic in Marseilles (around 1 million
inhabitants)
Monomodal model with an equilibrium auto
assignment of an aggregated matrix
In the frame of a work for the private company
operating the only toll infrastructure in Marseilles, it
was necessary to calibrate it in time (in order to
update the optimal toll)
Possibility to assign depending on 2 users’ classes
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CETE
Starting point - n°2
Méditerranée
Model process overview
Populations
Jobs
OD matrices of
daily motorized
trips by 3 main
purposes
GENERATION
Daily emissions assessed in motorized trips
Daily attractions assessed in motorized trips
DISTRIBUTION (1)
TIME OF DAY
OD matrices of motorized trips
for the evening peak hour
given by purpose and mode
MODAL SPLIT
1 OD matrix aggregated
in vehicles
VEHICLE OCCUPANCY
ASSIGNMENT
Reproduction of traffic for the evening
peak hour (flows, travel time, path
analyses …)
(1) Entropic distribution model based on distance table calibrated for the 3 different trip purposes
5/31
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Starting point - n°3
Méditerranée
Calibration of the predicted vs observed flows
(around 100 measurement points)
Calibration of the aggregated matrix in 10*10 zones
Calibration of travel times (it was in 1993 !)

Forecasts based on :
an increase of the total demand of 4%
- an increase of the internal demand of 2%
- tests done on future scenarios with or without new
infrastructures
-
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Méditerranée
Starting point - n°4
Model forecasts overview
Traffic simulations indicating benefits of a new express
road, even for the internal demand :
Future scenario without the express road (in comparison with the actual scenario)
Increase of +66% on average travel time
Increase of +25% on average travel length
Increase of +77% on veh*h
Increase of +28% on veh*km
=> + 4.5 km/h lost on average speed
Future scenario with the express road (in comparison with the actual scenario)
Smaller increase on average travel time (+49% / +66%)
A slightly higher increase on average travel length (+28% / +25%)
Smaller increase on veh*h (+56% / +77%)
A slightly higher increase on veh*km (+31% / +28%)
=> + 2km/h gained on average speed in comparison with the situation
without the new infrastructure
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Starting point - n°5
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Targets
Drive access to activities
Socio-economic assessments based on the results of such
studies
 Models always indicate benefits associated with new facility
Traffic induction
Urban spreading questioning
Driving force
Economic approach in the field of individual time management
Zahavi researches and co
Stability observed locally (Marseilles) for motorized average
travel time for evening peak hour
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Starting point - n°6
Méditerranée
Issue
Analysis of the last household surveys
 conclusions opposed to traffic forecasts :
For the past decade, observed data to conclude to :
- non significant evolutions for average travel time
- a rather stable average travel length
- a higher rate for motorized mobilities evolution
(conjectural)
- an increase for veh*km due to mobility, but not due
to a raise of average travel length
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Méditerranée
Starting point - n°7
Approach principles
introduce an average travel time constraint
 control distribution thanks to this constraint
 feedback of assignment on distribution
 aim : to calibrate the distribution model with an
entropic formula depending on travel times resulting
from assignment
GENERATION
DISTRIBUTION
MODAL SPLIT
ASSIGNMENT
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Demand matrix
Traffic assignment results
CETE
Process implementation - n°1
Méditerranée
Modeling framework
matrix aggregated in vehicles
for evening peak hour
Vehicles emissions and attractions
for the evening peak hour
COMBINED ASSIGNMENT
DISTRIBUTION MODEL
CALIBRATION (2)
Reproduction of traffic for the
evening peak hour under the
constraint on travel times
(2) Entropic distribution model based on travel times
11/31
CETE
Process implementation - n°2
Méditerranée
Algorithm based on :
Furness and Fratar method for distribution problem
resolution under entropic model,
-
Frank and Wolf linear approximation method for solving
equilibrium assignment problem under Wardrop
principle,
-
Partial linear approximation of Frank and Wolf method
for solving the combined trip assignment-distribution
problem (S.P. Evans)
-
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CETE
Process implementation - n°3
Méditerranée
Op
Dp
DISTRIBUTION MODEL (with fixed )
Gpq
TEST
Network
codification
Assignment algorithm
Va
Global principle
Upq
1/ Entropic distribution model depending on
exp(-*free_flow_time) of emissions and
attractions calculated formerly provides the
first OD matrix (Gpq)
2/ Equilibrium assignment of this matrix gives
the flows on segments. A travel time matrix is
also calculated.
3/ Distribution based on the entropic model
applied to the travel time matrix obtained at the
previous step (assignment) gives a new OD
matrix.
4/ The difference between step1 and step3
demand matrices entails to test the
convergence of the iterative process.
5/ If the test fails, that is to say that the
convergence is not enough, so the process has
to continue by the successive averages method
applied to the demand matrices (and flows as
well)
6/ The assignment of the resulting matrix on a
network pre-assigned with the resulting flows
provides the travel time matrix
Back to step 3
This process is known as convergent
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…
CETE
Process implementation - n°4
Méditerranée
In practice, an algorithm implementing :
2 iterative processes
The first one :
at fixed, research of convergence of the
combined distribution-assignment processes
-
stopping criteria depending on the stability of the
demand matrix resulting of the process between 2
steps
-
-
successive averages principle
introduction of a 3 D distribution with a travel times
histogram
-
14/31
CETE
Process implementation - n°5
Méditerranée
The second one :
makes  evolved with the postulate that the
average travel time calculated at a given  is a
decreasing function of 
-
stopping criteria depending on the proximity
between the predicted average travel time and the
observed value
-
15/31
CETE
Process implementation - n°6
Méditerranée
Calcul of  0 (for instance
1/observed average travel time)
Equilibrium
assignment of the
basic model we
have in charge
And the observed travel times
histogram for step0
volau Assignment0
Travel
time
matrix
Distribution 3D y
New internal demand matrix
Index function given
travel times histogram
volau=new_volau
x=x+1
volau
no
test1
x=0
Calcul of y+1
no
New internal demand matrix
New_volau
yes
Calcul Travel time
matrix (assignment 0)
test2
New internal demand matrix
yes
New volau
New travel time matrix
Distribution 3D with y
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Test1 = stability between two x step of the
resulting demand
Test2 = proximity with the observed
average travel time
CETE
Process implementation - n°7
Méditerranée
25000
20000
A data panel not accurate
enough
15000
10000
5000
0
0
10
20
30
40
50
60
25000
20000
15000
10000
5000
0
0-5
5-10
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-50
50-55
55-60
40000
An average travel time calculated
around 21.42
35000
30000
25000
20000
15000
A confidence level >20%
10000
5000
0
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0-10
10-20
20-30
30-40
40-50
50-60
CETE
Process implementation - n°8
Méditerranée
The constraint controlling the test of the iterative
calibration of  is, not only the average travel time
(which is not accurate enough), but also, the travel
times histogram
30 000
25 000
20 000
15 000
10 000
5 000
0
0à10
18/31
10 à 20
20 à 30
30 à 40
40 à 50
50 à 60
CETE
Results - n°1
Méditerranée
Analysis of the process implementation
Research of  and evolution of the average
travel time
19.3
19.2
mn
19.1
19
18.9
18.8
18.7
1
2
3
4
5
6
7
step
19/31
8
9
10
11
12
13
14
CETE
Results - n°2
Méditerranée
Analysis of the process implementation
Fast convergence of the combined processes
0.3
max des erreurs relatives
0.25
0.2
0.15
150
0.1
130
0.05
0
moy ds erreurs relatives
110
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
step
90
70
50
30
20/31
step
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
7
10
-10
4
1
10
CETE
Results - n°3
Méditerranée
Analysis of the process implementation
A good reproduction of the travel times histogram
whatever combined processes step
EMD ;moy=21.42
30 000
Ancienne dist ; moy=22.21
25 000
Nelle dist ; moy=18.94
20 000
Nelle dist ; moy = 19.21
15 000
10 000
5 000
0
0à10
21/31
10 à 20
20 à 30
30 à 40
40 à 50
50 à 60
CETE
Méditerranée
Results - n°4
Process implementation analysis
Evolution of predicted flows depending on the
combined processes step
flow differences <2%
(but it can reach a value
around 200 veh/hps on
some segments)
Other Traffic results
differences <6% (veh*km ;
veh*h)
22/31
Differences between predicted flows of the
combined processes at step1 with the predicted
flows of the combined processes at step 15
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Results - n°5
Comparison between the combined processes results
and the step0 matrix assignment results
Travel times histogram analysis
(already discussed)
Traffic analysis
assignment results :
23/31
Differences between combined processes
predicted flows and step0 matrix assignment
results
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Méditerranée
Results - n°6
Comparison between the combined processes results
and the step0 matrix assignment results
Analysis of predicted vs observed flows
24/31
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Results - n°7
Comparison between the combined processes results
and the step0 matrix assignment results
Analysis of internal demand matrices
Differences between combined processes
internal demand matrix and the step0 matrix
25/31
CETE
Results - n°8
Méditerranée
Comparison between the combined processes results
and the step0 matrix assignment results
Analysis of other traffics assignments results
- Average
travel time : -15%
- Average travel length : -2%
- veh*h : -10%
- veh*km : -3%
26/31
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Méditerranée
Results - n°9
Comparative analysis on traffic forecasts
between the combined processes results and
the step0 matrix assignment results
Analysis on predicted flows
27/31
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Results - n°10
Comparative analysis on traffic forecasts between the
combined processes results and the step0 matrix
assignment results
Future scenario without the express road (in comparison with the actual scenario)
Average travel time constrained to be stable
A rather stable average travel length evolution (slight decrease)
Veh*km and veh*h decreasing slightly
Average speed stable between the future and the actual scenario
Future scenario with the express road (in comparison with the actual scenario)
Average travel time constrained to be stable
A rather stable average travel length evolution
A slight increase of the veh*km and veh*h
Average speed increased only by 1 km/h
=> Minor benefits with the new facility
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29/31
Back to the questions at stake
For now, work limited to a new distribution (emissions and
attractions constrained by the totals of the step0 matrix)
 A potential process to test urban spread, but with other
researches
Feedback of assignment on distribution (for the internal
matrix)
 One way to take into account the effect of the limitation of
the offer on the demand
A more centered matrix, future scenarios with less
degradation of the traffic conditions
 Combined processes non-necessarily indicate benefits for
a new facility
Combined processes providing a mean to take into
account the effects of a new infrastructure on reports with
induction
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Cautions and discussions - n°1
Warnings :
Process experimented on the internal demand limited to
a very urban perimeter
Monomodal aggregate model
Non accurate data
To go further :
Test sensitivity (offer, transport policies, demo-economic
evolutions)
Comparisons with empirical formulae of traffic induction
What if the perimeter is larger ?
Working with emission and attraction totals calculated
with a work on mobilities and modal split
Calibrate different  for each trip purpose
What if the model is multimodal ?
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Méditerranée
Cautions and discussions - n°2
A potential :
A mean to test new facilities in regard to drive access
to activities and urban spread
Conclusions :
One help for decisions in a financial constrained
world and with urban spreading for which parameters
can no longer be exogenous (impact of offer on
demand)
Bases for a work on accessibility
An approach entailing to a work on mobilities
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